Contact the Urban Justice Center, they are in upper Manhattan and they are listed in the phone book/directory assistance. They can help you out, they deal with the homelesss, specifically the disabled homeless.

I am not sure if this applies anymore, but homeless families used to be priority candidates for low income housing. Go to your local New York City Housing Authority Office and see if you qualify for Section 8, if you do, fill out the applications and everything. Once you get your Section 8 certificate you can then apply for low income housing. The eviction on your record would be a problem, but if you are homeless with children, you are still an emergency case and you may be able to get around it. Another place to go is Catholic Charities. They are also listed in the phone book. Ask about Providence Houses. You can also ask around at your church,if you are Christian, especially if you are Catholic. A lot of times, a clergyman will intervene and help you network to find a safer place to live in. The same may be true if you are Muslim or Jewish, your mosque or synagogue may have contacts that can help you find a better place to go. You can also call up Social Services and find out how you and your family can be transferred to a Tier 2 shelter. These facilities are like apartments and are cleaner and more spacious (and in some cases safer) for people who have children. YOu can ask about this at the local welfare office, or whereever you go to pick up your SSI or disability checks.